Morse potential parameters

During initialization and final analysis of the QCT calculations, the numerical values of the Morse potential parameters that we have used are given as De = 4.580 eV, re = 0.7416 A, and (3 = 1.974 A-1. Moreover, the potential energy as a function of internuclear distances obtained from the analytical expression (with the above parameters) and the LSTH [75,76] surface asymptotically agreed very well. 

Figure 3.23 Collision numbers for CO and the halogen compared with experimental data of other investigators (see text). Solid lines semidassical theory with Morse potential parameter and chosen for best fit broken lines SSH theory, method B, using Lennard-Jones parameters and Za = 3.

Morse Potential Parameters for Triatomic van der Waals Molecules... 

We can write these same equations in terms of the Morse potential parameters and fx by using Eq. (2.49) ... 

Table I Morse potential parameters for the ChHe and Cl2He2 PES (for the excited B electronic state) used in this work.

ESTIMATION OF MORSE POTENTIAL PARAMETERS FROM THE CRITICAL CONSTANTS AND THE ACENTRIC FACTOR. 

Morse potential parameters 13,14 oxidation—see Oxidation, of thiols photoelectron spectrum 28, 30 photolysis of, condensed phase 471-A16... 

Hartree-Fock limit 52 heat of formation 31 hydride aflBnity 31, 81, 82 hydrogen aflBnity 31, 81, 82 ionization potmtial 79, 80 Morse potential parameters 10, 24-26... 

Figure 22.3 The Vibrational Potential Energy and Energy Levels of the CO Molecule, (a) The vibrational potential energy represented by the Morse function, (b) The first 20 vibrational energy levels for the Morse potential. The Morse potential parameters for COareDe = 11.2eV= 1.80 x 10 J and a = 2.2994 x 10 ° m". The force constant for the harmonic potential is /c = 1900N m-T...

Additionally to and a third adjustable parameter a was introduced. For a-values between 14 and 15, a form very similar to the Lennard-Jones [12-6] potential can be obtained. The Buckingham type of potential has the disadvantage that it becomes attractive for very short interatomic distances. A Morse potential may also be used to model van der Waals interactions in a PEF, assuming that an adapted parameter set is available. 

Here, Dg is the bond dissoeiation energy, rg is the equilibrium bond length, and a is a eonstant that eharaeterizes the steepness of the potential and determines the vibrational frequeneies. The advantage of using the Morse potential to improve upon harmonie-oseillator-level predietions is that its energy levels and wavefunetions are also known exaetly. The energies are given in terms of the parameters of the potential as follows ... 

Although two-parameter models are rather restrictive, three-parameter models of the intermolecular potential have been developed which provide reasonable descriptions of the thermodynamic behavior of solids. Examples include the Morse potential, the exponential-six potential, and, more recently, a form proposed by Rose et al. (1984) for metals. 

Morse potential). The constant C is defined such that t/ (r) = 0 at the cutoff distance R. The interaction range is determined by the parameter a, which Viduna et al. choose very large, a = 24. Hence the cutoff distance can be made small (R = 1.25cr in [144]). This model was first used by Gerroff et al. [147] and is discussed in some detail in Chapter 12 of this book. 

There are a number of three- to five-parameter potential functions in the literature, of which the Morse potential is the most popular a typical five-parameter potential is the Linnett function (Linnett, 1940, 1942) ... 

For each bond type, i.e. a bond between two atom types A and B, there are at least two parameters to be determined, and /fg . The higher-order expansions and the Morse potential have one additional parameter (a or D) to be determined. 

A third functional form, which has an exponential dependence and the correct general shape, is the Morse potential, eq. (2.5). It does not have the dependence at long range, but as mentioned above, in reality there are also R, /f etc. terms. The D and a parameters of a Morse function describing vdw will of course be much smaller than for str, and Ro will be longer. 

It is interesting to note that the simple Morse potential model, when employed with appropriate values for the parameters a and D (a = 2.3 x 1010 m 1, D = 5.6 x 10 19 J as derived from spectroscopic and thermochemical data), gives fb = 6.4 nN and eb = 20%, which are quite comparable to the results obtained with the more sophisticated theoretical techniques [89]. The best experimental data determined on highly oriented UHMWPE fibers give values which are significantly lower than the theoretical estimates (fb 2 nN, b = 4%), the differences are generally explained by the presence of faults in the bulk sample [72, 90] or by the phonon concept of thermomechanical strength [15]. 

Some additional comments regarding Equation 4 are in order. The factor 143.88 converts the units to kcal/mol. There are two additional constants. The first is ks, which is the stretching force constant parameter in units of md A 1. The second constant is cs, which is the cubic term with a unitless value of 2.55. When a Morse potential is expanded in a power series, the factor 7/12 is obtained. 

Here Eh and a are the parameters of a normal Morse potential, and m = mh mi in the framework of the model discussed). Although this combined potential (4.3.26) provides plausible estimates, it can hardly be substantiated in terms of the theory of intermolecular interactions and contains, in addition, only biquadratic anharmonic... 

Many other useful forms have been proposed (Steele and Lippincott, 1962) and their parameters were related to spectroscopic constants as will be given for the Morse potential by Eq. (1.14). Quite often, the potential V(r) is expanded as a power series in the displacement from equilibrium (force field method)... 

These equations provide an explicit relationship between the parameters appearing in the Morse potential, re, 3, V0, and the reduced mass (i and the algebraic parameters E 0, A, B, and N. Particularly important is the relation N + 2 = 2a, which shows explicitly how the vibron number N is related to the number of bound states in the potential of Figure 2.8. 

We thus find once more that, if we use a Morse potential, its range parameter P is given by Eq. (7.124),... 

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